I am under the impression that the dimensions of sector shaped conductor, including segments for Milliken conductor, are determined by using geometry in the Product Engineering Department of each Wire and Cable Company. The massaged geometric shapes are outlined with black ink, full size on clear film. Then, when segments are rolled, they are compared to the design master (film) with an optical comparator. If the segments appear OK, they are then closed to determine how the overall conductor fits together. If OK, it is a go, but if it is not OK, the segment shapes may have to be adjusted and the whole process done again.

I seriously doubt that any Wire and Cable Company is going to give away or publish their intellectual property in this regard.

Typically a customer had a corner radius that they either wanted or needed and ordered the wire with that spec. We would make a cross section mount and like you said, use optical comparator to check the corners. Once you knew the corner radii, you could calculate the cross sectional area. If the wire was 0.100 x 0.400 and the specified corner radius was 0.015 then if you multiplied width x thickness (assuming near 0.00 corner radius, the area would be 0.0400. Now you need to calculate the material missing due to the corner radius. Think a circle inside a box. The box would be (.015 + 0.015) squared. Subtract the area of the circle from the box; 3.1417 x 0.15 squared. That number is then subtracted from 0.0400 and what is left is the cross sectional area.

I was however thinking more along the lines of power cable and building wire with segmented shaped conductor. Take a look at the five segments in the Milliken conductor photograph at
www.stewart-hay.com/plant1ie.htm
The segment is pretty tricky to design because each must slide past each other during the final closing process. The particular conductor in the picture is even more difficult because the aluminum wires were hard drawn and thus the sectors were quite rigid and a bit springy. There is a lot of process technique to get the conductor properly closed.

Peter, thanks for the card. I didn't bother to check what sector shaped cable was. Besides making and coating very fine wires like 50 awg and smaller diameter, probably one of the most difficult magnet wire products to make was transposed cable. I never worked with making any but with company making the shaped wire that went into making it. Did you ever do any transposing?

Yes our magnet plant in Simcoe, Ontario manufactured transposed cable for many decades and still does. (J. A. Kraft machinery as I recall.) The plant was later sold to Superior Essex, now 100% owned by LS Cable & System of Seoul, Korea and thus a private company.